Practical Ship Hydrodynamics

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32 Practical Ship Hydrodynamics R R P P Grid spacing Fine (h) Medium (2h) Coarse (4h) R P R R P P Figure 1.5 Multigrid cycles: V-cycle (left), W-cycle (right), h: grid spacing P R Prolongation Restriction computations more than justifies the additional expense of programming and storage requirements. Therefore most newer developments for RANSE codes for ship flows include multigrid methods. 1.5.6 Numerical approximations Finite-volume methods require values (and derivatives) of various variables at the cell faces, when they are originally only known at the cell centres. The flow direction is often considered when these quantities are determined for convective terms. Time derivatives are also numerically approximated. Consider, e.g., the convective fluxes in the x direction. One determines in general the value of a variable (e.g. pressure of velocity) at the location x by employing an interpolation polynomial through the neighbouring cell centres xi: f⊲x⊳ D a1 C a2⊲x x1⊳ C a3⊲x x1⊳⊲x x2⊳ CÐÐÐ The coefficients ai are determined by inserting the known function values fi D f⊲xi⊳. The most simple case uses just the value of the next cell centre upstream (upwind differencing scheme, UDS ): f⊲x⊳ D fi 1 u>0 f⊲x⊳ D fi u
Introduction 33 flow direction. CDS tends to numerical instabilities and is therefore for usual discretizations and speeds unsuited for the approximation of the convective fluxes; the diffusive terms are usually approximated by CDS. The linear upwind differencing scheme (LUDS) uses the cell centres of the next two upstream points: f⊲x⊳ D fi 2 fi 1 ⊲x xi 1⊳ C fi 1 u>0 xi 2 xi 1 f⊲x⊳ D fi fiC1 ⊲x xi⊳ C fi u0 1 8 ⊲fiC1 C fi 1 2fi⊳ u
Page 1 and 2: Practical Ship Hydrodynamics
Page 3 and 4: Butterworth-Heinemann Linacre House
Page 5 and 6: 3 Resistance and propulsion .......
Page 7 and 8: 5.4.5 Interaction of rudder and shi
Page 9 and 10: Preface The first five chapters giv
Page 11 and 12: 1 Introduction Models now in tanks
Page 13 and 14: Introduction 3 certain investigatio
Page 15 and 16: Introduction 5 there have been prop
Page 17 and 18: Introduction 7 is a material consta
Page 19 and 20: Introduction 9 margin may make a di
Page 21 and 22: Introduction 11 solution either. Ev
Page 23 and 24: Introduction 13 in naval architectu
Page 25 and 26: Introduction 15 ž Finite differenc
Page 27 and 28: Introduction 17 makes seakeeping pr
Page 29 and 30: Introduction 19 ship. Inner flow co
Page 31 and 32: Introduction 21 performed on workst
Page 33 and 34: Introduction 23 experts, while boun
Page 35 and 36: Introduction 25 two more decades be
Page 37 and 38: Introduction 27 Figure 1.3 A cylind
Page 39 and 40: Introduction 29 resolved by conside
Page 41: Introduction 31 ž LSOR (line succe
Page 45 and 46: Introduction 35 equation, i.e. the
Page 47 and 48: 2 Propellers 2.1 Introduction Ships
Page 49 and 50: Propellers 39 ž rake iG The face o
Page 51 and 52: KT KQ h 10 . K Q K T Figure 2.3 Pro
Page 53 and 54: Propellers 43 methods or panel meth
Page 55 and 56: Propellers 45 This formula can be i
Page 57 and 58: Propellers 47 power. The earliest l
Page 59 and 60: Propellers 49 corrected subsequentl
Page 61 and 62: Propellers 51 flow computations are
Page 63 and 64: Propellers 53 occurs earlier, as ca
Page 65 and 66: Propellers 55 2.5.2 Open-water test
Page 67 and 68: Propellers 57 the traditional prope
Page 69 and 70: Propellers 59 (model/full-scale shi
Page 71 and 72: Propellers 61 represents the cavity
Page 73 and 74: Resistance and propulsion 63 1. The
Page 75 and 76: Resistance and propulsion 65 3.1.2
Page 77 and 78: Figure 3.3 Double-body flow y Wave
Page 79 and 80: Resistance and propulsion 69 course
Page 81 and 82: Resistance and propulsion 71 limite
Page 83 and 84: Table 3.1 Recommended values for CA
Page 85 and 86: Resistance and propulsion 75 3.2.6
Page 87 and 88: P B ⋅ 10 3 (kW) 40 30 20 10 0 n P
Page 89 and 90: Resistance and propulsion 79 t is t
Page 91 and 92: Resistance and propulsion 81 are no
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3.4 Simple design approaches Resist
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Resistance and propulsion 85 of the
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Resistance and propulsion 87 non-li
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Resistance and propulsion 89 resist
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Resistance and propulsion 91 (doubl
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Resistance and propulsion 93 only b
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Resistance and propulsion 95 resist
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Resistance and propulsion 97 1°. S
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Ship seakeeping 99 3. Addition of t
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Ship seakeeping 101 1. No recording
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Ship seakeeping 103 Re denotes the
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Ship seakeeping 105 the ship axis x
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Ship seakeeping 107 The procedure t
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Ship seakeeping 109 If several ω r
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a 0.015 0.010 0.005 0 1 2 3 4 5 Uc/
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Ship seakeeping 113 The (only stati
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Ship seakeeping 115 height H1/3 for
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Ship seakeeping 117 using data of B
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Ship seakeeping 119 for each strip
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Ship seakeeping 121 between near fi
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Ship seakeeping 123 wave length of
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Ship seakeeping 125 The elements of
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Ship seakeeping 127 4.4.3 Rankine s
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Ship seakeeping 129 to zero. Then t
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Ship seakeeping 131 for commercial
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Ship seakeeping 133 Since the spect
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Ship seakeeping 135 ž The ωj are
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Ship seakeeping 137 changing sea sp
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Ship seakeeping 139 The wave impact
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Ship seakeeping 141 pressure gauges
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v(t) h(x,t) y u(x,t) Figure 4.23 On
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Ship seakeeping 145 computations wi
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Ship seakeeping 147 4. Derive the p
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Ship seakeeping 149 The free consta
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5 Ship manoeuvring 5.1 Introduction
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Ship manoeuvring 153 ž yaw rate (r
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Ship manoeuvring 155 Table 5.2 Non-
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Ship manoeuvring 157 but also the i
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C y 1.50 1.25 1.00 1.75 0.85 0.80 0
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Ship manoeuvring 161 section. The l
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Ship manoeuvring 163 methods have b
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esistance R is proportional to spee
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Ship manoeuvring 167 accuracy, but
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Ship manoeuvring 169 the difference
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Ship manoeuvring 171 it is importan
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d, y 20° 10° 0° −10° −20°
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Distance Lateral deviation Length o
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Ship manoeuvring 177 also performed
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Ship manoeuvring 179 ž Rudders out
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ehind the leading edge (nose) is: c
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Ship manoeuvring 183 the rudder. In
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Ship manoeuvring 185 attack ˛ of n
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V a /V 0.4 0.3 0.2 0.1 V a /V 2.0 1
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Ship manoeuvring 189 ž Rudder with
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average between VA and V1: � �
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C L (V corr ≠ V A ) C L (V corr =
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Ship manoeuvring 195 hull influence
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Ship manoeuvring 197 - Estimate the
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Ship manoeuvring 199 rudder tip vor
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Ship manoeuvring 201 (1993) uses de
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Ship manoeuvring 203 ž Profiles wi
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Ship manoeuvring 205 The ship perfo
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6 Boundary element methods 6.1 Intr
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C ⊲t1n3 C n1t3⊳⊲t3 xxz C s3 x
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xx D ⊲ 3 x⊲x xq⊳ ⊳/r 2 xy D
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The velocity in the x direction is:
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∂ ∂z Boundary element methods 2
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Boundary element methods 217 2. Thr
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and ⊲ , ⊳ is: r D � ⊲x ⊳
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⊲1⊳ y D � d 2 y d r 2 f ⊲c
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Boundary element methods 223 the so
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2 0 8xz D 2 2 0 8xxz D 2 2 0 8xzz D
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Figure 6.9 Velocities induced by po
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It is convenient to write ϕ as:
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Boundary element methods 231 usuall
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Boundary element methods 233 From t
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with: Boundary element methods 235
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Numerical example for BEM 237 S is
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Numerical example for BEM 239 In ea
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Numerical example for BEM 241 Once
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Numerical example for BEM 243 ž Tr
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Numerical example for BEM 245 that
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Numerical example for BEM 247 is ch
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Table 7.1 Sign for derivatives of p
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z y Figure 7.5 Coordinate system us
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the contour (Fig. 7.5): n� iD1 i
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Numerical example for BEM 255 Let E
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Numerical example for BEM 257 At th
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Numerical example for BEM 259 This
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Numerical example for BEM 261 The i
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Numerical example for BEM 263 The e
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References Abbott, I. and Doenhoff,
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References 267 Morgan, W. B. and Li
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Index Actuator disk, 44 Added mass,
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Practical Ship Hydrodynamics

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